Topics in Algebraic and Topological K-Theory

Author: Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher: Springer Science & Business Media
ISBN: 3642157076
Category: Mathematics
Page: 308
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This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Space – Time – Matter

Analytic and Geometric Structures
Author: Jochen Brüning,Matthias Staudacher
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110452154
Category: Mathematics
Page: 517
View: 8768

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This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

2016 MATRIX Annals

Author: Jan de Gier,Cheryl E. Praeger,Terence Tao
Publisher: Springer
ISBN: 3319722999
Category: Mathematics
Page: 656
View: 7338

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MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: Higher Structures in Geometry and Physics (Chapters 1-5 and 18-21); Winter of Disconnectedness (Chapter 6 and 22-26); Approximation and Optimisation (Chapters 7-8); Refining C*-Algebraic Invariants for Dynamics using KK-theory (Chapters 9-13); Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology (Chapters 14-17 and 27). The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

Algebraic K-Theory and Its Applications

Author: Jonathan Rosenberg
Publisher: Springer Science & Business Media
ISBN: 9780387942483
Category: Mathematics
Page: 394
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Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.

Lecture Notes in Algebraic Topology

Author: James Frederic Davis,Paul Kirk
Publisher: American Mathematical Soc.
ISBN: 0821821601
Category: Mathematics
Page: 367
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The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Handbook of K-Theory

Author: Eric Friedlander,Daniel R. Grayson
Publisher: Springer Science & Business Media
ISBN: 354023019X
Category: Mathematics
Page: 626
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This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Algebraic K-Theory

Author: Vasudevan Srinivas
Publisher: Springer Science & Business Media
ISBN: 0817647368
Category: Mathematics
Page: 341
View: 9020

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Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.

Topics in K-Theory

The Equivariant Künneth Theorem in K-Theory. Dyer-Lashof operations in K-Theory
Author: L.H. Hodgkin,V.P. Snaith
Publisher: Springer
ISBN: 3540380264
Category: Mathematics
Page: 294
View: 9363

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Introduction to Algebraic K-theory

Author: Elias Milnor,John Willard Milnor,Milnor John,John N. Mather
Publisher: Princeton University Press
ISBN: 9780691081014
Category: Mathematics
Page: 184
View: 2032

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Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Algebraic K-Theory

Author: Richard G. Swan
Publisher: Springer
ISBN: 3540359176
Category: Mathematics
Page: 264
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From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."

Algebraische Topologie

Homologie und Mannigfaltigkeiten
Author: Wolfgang Lück
Publisher: Springer-Verlag
ISBN: 3322802418
Category: Mathematics
Page: 266
View: 6592

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Hauptgegenstand des Buches sind Homologie-, Kohomologietheorien und Mannigfaltigkeiten. In den ersten acht Kapiteln werden Begriffe wie Homologie, CW-Komplexe, Produkte und Poincaré Dualität eingeführt und deren Anwendungen diskutiert. In den davon unabhängigen Kapiteln 9 bis 13 werden Differentialformen und der Satz von Stokes auf Mannigfaltigkeiten behandelt. Die in Kapitel 14 und 15 behandelte de Rham Kohomologie und der Satz von de Rham verbinden diese beiden Teile.

An Introduction to K-Theory for C*-Algebras

Author: M. Rørdam,Flemming Larsen,N. Laustsen
Publisher: Cambridge University Press
ISBN: 9780521789448
Category: Mathematics
Page: 242
View: 9766

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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

Michael Atiyah Collected Works

Volume 2: K-Theory
Author: Michael Atiyah
Publisher: Oxford University Press
ISBN: 9780198532767
Category: Language Arts & Disciplines
Page: 854
View: 8217

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One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.

Algebraic and geometric topology

proceedings of a conference held at Rutgers University, New Brunswick, USA, July 6-13, 1983
Author: Andrew Ranicki,Norman Levitt,Frank Quinn
ISBN: 9783540152354
Category: Mathematics
Page: 423
View: 3930

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Poincarés Vermutung

die Geschichte eines mathematischen Abenteuers
Author: Donal O'Shea
Publisher: N.A
ISBN: 9783596176632
Page: 376
View: 8584

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